Synthesis of Optimal Correction Functions in the Class of Disjunctive Normal Forms
Kabulov A. Baizhumanov A. Saymanov I.
July 2024Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2024#12Issue 13
The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, problems arise that are close in methodology to the problems of synthesizing reliable circuits from unreliable elements or making a collective expert decision. The work solves the problem of constructing an optimal correction function based on control material; classes of functions of k-valued logic under monotonicity restrictions are studied. A theorem on the completeness of the class of monotonic functions of k-valued logic for arbitrary k is proved, and a basis in the given class is proved and constructed. The problem of constructing an optimal corrector in the class of disjunctive normal forms of k-valued functions is solved.
disjunctive normal forms , k-valued function , logic function , logical separability problem , minimization , monotone , optimal correction function
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School of Mathematics and Natural Sciences, New Uzbekistan University, Mustaqillik Ave. 54, Tashkent, 100007, Uzbekistan
Applied Mathematics and Intelligent Technologies Faculty, National University of Uzbekistan, Tashkent, 100174, Uzbekistan
Department of Mathematics, O. Zhanibekov South Kazakhstan State Pedagogical University, A. Baitursynov Street No.13, Shymkent City, 160012, Kazakhstan
School of Mathematics and Natural Sciences
Applied Mathematics and Intelligent Technologies Faculty
Department of Mathematics
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